i need to solve this equation by completing the square:

Question

x^2-14x+1=0

i don't' know how to do this, nor do i know what complete the square means.
please help.

Answer 1

x^2-14x+1=0
take the constant to the other side
x^2-14x = -1

now you want to turn the left side into a perfect square,
take 1/2 of the x term coefficient, then square it, and add it to both sides

x^2 - 14x + 49 = -1 + 49
now the left side is a perfect square
(x-7)^2 = 48
take the square root of both sides
x-7 = ±√48
x = 7 ±4√3

Answer 2

So is that the same way you'd do 3x^2+9x-12=0?

Answer 3

yes, you could, but divide each term by 3 first, if it says "solve by completing the square"

on the other hand it factors quite nicely
3x^2+9x-12=0 divide by 3
x^2 + 3x - 4 = 0
(x+4)(x-1) = 0
x = -4 or x = 1

Answer 4

So what if you were factofing 2x^2-x-35=0?